I have just spent half an hour with my son and the internet. As a student, he has access to websites I don't. We couldn't find anything of any real use. But talking with him, we think we have worked out what Seachem mean.
Most American water suppliers use chloramine instead of chlorine as a disinfectant as do some, but not all, UK water companies. Chloramine is chlorine and ammonia joined together. All dechlorinators contain thiosulphate which reacts with chlorine and prevents it harming the filter bacteria. With chloramine, it removes the chlorine part and leaves the ammonia half of the molecule in the water. Prime and other dechlorinators contain a chemical (and we failed to find what it is!) that binds this ammonia. It is not ammonia made by the fish, it is ammonia that comes from tapwater. This ammonia-Prime complex slowly breaks down and liberates ammonia which is then detected by our test kits. We are reasoning that Seachem say you get a false reading after the complex breaks down is just because you are measuring the ammonia that comes from the tapwater and not ammonia made by the fish.
Of course, if for some reason you have a lot of ammonia made by the fish in the tank water - because you are cycling or had a problem with the filter - that will be treated the same as the ammonia from chloramine. It will be bound by whatever it is in Prime then released again slowly. This is why the advice is always to not rely on this type of dechlorinator during a fish-in cycle as the effect only lasts a day or two.
So the answer to your question is - if you have just chlorine in your tapwater it shouldn't make any difference when you test as the only ammonia in the tank will be from your fish which should only be present in a trace amount too low for our testers to pick up. If you are worried about checking to make sure your filter is working properly, wait a day or two after a water change, then test.
But if you have chloramine, if you test immediately after a water change, you'll get a reading which does not include the ammonia from chloramine - but it will also not measure any ammonia from the fish if the filter has a problem. After a couple of days, you might get an ammonia reading but that would most likely be the chloramine-ammonia. If the filter is working properly, that will be removed pretty quickly by the filter. The best time to test for ammonia if you do have chloramine is a few days after a water change.
I'm typing this while surrounded by people talking - if I haven't made sense, tell me
